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Computing a Nash equilibrium (NE) is a central task in computer science. An NE is a particularly appropriate solution concept for two-agent settings because coalitional deviations are not an issue. However, even in this case, finding an NE is PPAD-complete. In this paper, we combine path following algorithms with local search techniques to design new algorithms for finding exact and approximate NEs. We show that our algorithms largely outperform the state of the art and that almost all the known benchmark game classes are easily solvable or approximable (except for the GAMUT CovariantGameRand class).
The combination of deep reinforcement learning and search at both training and test time is a powerful paradigm that has led to a number of successes in single-agent settings and perfect-information games, best exemplified by AlphaZero. However, prio
Computing Nash equilibrium in bimatrix games is PPAD-hard, and many works have focused on the approximate solutions. When games are generated from a fixed unknown distribution, learning a Nash predictor via data-driven approaches can be preferable. I
We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given strategy. These
Extensive study on the complexity of computing Nash Equilibrium has resulted in the definition of the complexity class PPAD by Papadimitriou cite{Papa2}, Subsequently shown to be PPAD-complete, first by Daskalakis, Goldberg, and Papadimitriou cite{Pa
Coordination games describe social or economic interactions in which the adoption of a common strategy has a higher payoff. They are classically used to model the spread of conventions, behaviors, and technologies in societies. Here we consider a two